Consider the Roy economy discussed in class, in which workers have het- erogeneity in skills employed in different sectors. Assume that the skill of a worker as hunter, m is drawn from a Uniform distribution on the (0,10) interval, and the skill of a worker as a sherman, 1.52 is drawn from a Uniform distribution on the (0,10) interval, independent of how large is his skill level as a hunter. Assume that the wage is the product of the worker skill times the price of the product (which is always true if we measure skill by the number of pounds of meat the worker can obtain in a given day). Assume that the price of meat 1:1 is 5, and the price of sh p2 is 5. Workers sort themselves into sectors based on their specic skill set. Assume that a worker chooses to hunt if, and only if, W1 > W2. That is, the worker chooses to hunt if his earnings as a hunter are larger than his earnings as a sherman. Denote by S the variable that indicates the worker's choice of sector: S equals one when the worker decides to hunt, and S equals 2 when the worker decides to sh. In other words: 8 1 ifW1>W2 2 ifW2>W1 Question 6 (20 points) a) What is the share of the population that will be employed in the hunting sector? That is, nd Pr[.5' = 1]. b) What is the expected value of earnings of a randomly choosen worker, if we force him to hunt? That is, nd E[W1]. c) What is the expected value of earnings of the workers that decide to hunt? That is, nd E[W1 IS = 1]. Is this larger than the number you found above? Why? d) What is the average skill level of someone that decides to hunt? That is, nd E['U,1|S = 1]. e) Consider someone to be a top-rated hunter if his skill as a hunter is greater than 90% of the rest of the population. Do the best hunters choose to hunt